IoannisXiotidis
Bs > μμ effective lifetime measurement
Introduction
In this section of my twiki the (effective lifetime measurement of the Bs>mumu decay) will be presented. The measurement of the effective lifetime has already been performed for the two other CERN experiments (CMS and LHCb) in their last publications for the Br(Bs>mumu) measurement but never for the ATLAS experiment. Theoretically, the measurement of the effective lifetime assumes that only Bh states decay in the SM making the precise measurement of the effective lifetime prompt to new physics.
Analysis Strategy
After an extensive discussion with my supervisor Prof. Alessandro Cerri the analysis strategy has been defined and presented in this section with the corresponding notes in the following 3 images.
The general overview is summarized in the following bullet list and in addition expanded a bit in the comments bellow:
 B+>JpsiK: mu4_mu6_Lxy0_Jpsimumu (trigger): Used as Control Channel
 Bs>mumu: mu4_mu6_Lxy0_Bmumu (trigger): Analysis channel
 Optimize (in BDT and ct) to minimize cτ uncertainty > BDT cut, ct range
 Branching fraction fit (from Fabio) > apply to single BDT bin > remove any dependence on ε, fs/fd > convert it into a Nsig fit and not Br
 Apply sPlot on fit result >
 ct histograms
 controls (Background, signal Pt, isolation, etc.)
 Consider fit in ct bins > mostly as cross check
 Fit MC signal distribution to data signal distribution with 1 parameter (cτ scale + resolution?)
We aim practically to have 3 passes over the above mentioned steps:
 Pass 1 (Use sPlot)
 Start with cut including two highest BDT bins
 ct histogram but also:
 Signal: Pt, Isolation
 Background: ct, Pt, isolation
 Compare with simulations
 Pass 2 (Explore systematics)
 Fit systematics (pulls, residuals, etc.)
 Build ct fit (cτ, cτ spreading parameter)
 Test on ToyMC > (cτ, σ) correction
 Bias ? (Pulls, residuals, low statistics)
 Pass 3 (Full analysis)
 Fit (m, cτ) in Data
 Compare with MC > validation
 Signal: m, cτ uncorrelated
 Background: ? > probably not we need to check
1) Used Channels
 B+>JpsiK: used as control channel for the analysis > the used trigger is the mu4_mu6_Lxy0_Jpsimumu
 Bs>mumu: used as the analysis channel > the used trigger is the mu4_mu6_Lxy0_Bmumu
Note: In those two channels the "luck" that we have two triggers that both have an Lxy0 cut is very fortunate. The reason for this is that the Lxy0 cut introduces a bias in the measurement of the lifetime, but since it's present in both triggers we are able to cancel the effect. To be honest this is not a direct cancelling of the effect since the two decays have a very different topology (the Jpsi muons don't point to the PV as the Bmumu) but it's a good thing to have it
2) Optimization
In order to progress with the analysis it is vital to optimize the cuts on BDT (we are going to use one BDT range since part of the sPlot technique is to not include variables that are dependent to the extracted distribution > for more information refer to the sPlot paper) and ct (in ct what we will obtain might be ct bins). The suggested up to now way of optimizing the BDT and the ct cuts are by attempting to minimize the cτ uncertainty. The optimization can be either performed in Data or in the combination of the signal and bb>mumuX MC, but it needs still to be defined.
3) Invariant mass fit
For this step our strategy is to benefit from the already existing fit created by F. Tresoldi for the Br(Bs>mumu) measurement in ATLAS. For the analysis using the 2015/2016 data, as we are planning to use, a simultaneous fit of Signal + Background in 4 BDT bins has been implemented which is more complicated than what we are planning to use for the effective lifetime measurement. Initially, we are not exactly sure whether we are going to bin in cτ and therefore it might be that a simultaneous fit is not required. In addition dependence on the parameters like signal efficiency, fs/fd etc. are not required. We need a simple fit that will measure the number of signal events (Nsig) and not the Br(Bs>mumu).
4) cτ plot extraction
Reaching this point of the analysis will bring us to make a decision regarding the method we plan to use for the effective lifetime measurement. The baseline plan at this stage which is also going to be mainly expanded to obtain the first result with the current data, is a technique called sPlot. Using this technique we will be able to extract the cτ histogram along with a set of control histograms that we are going to look at for cross check reasons (like Background: cτ, Pt, isolation. Signal: Pt, isolation etc.). The second possible method would be to perform a simultaneous fit in all the cτ bins that we created. The latter method mentioned is more complicated and dependent on the time we will have might be used as a cross check to the first of the two methods.
5) Extract result
A very different method than the two described in the papers of the two other experiments (CMS and LHCb) is planned to be used for the final fit. Instead of creating a fit model and perform a binned maximum likelihood fir on the cτ histogram obtained from the sPlot technique. We are planning to fir the MC signal distribution to the data signal distribution with 1 parameter (cτ scale + resolution). The inclusion of the resolution depends on the dependence of the resolution with the background (mainly). Multiple ways to evaluate this dependence have been discussed (usage of ToyMC).
Dataset and variables
In this section we present the datasets for the Bmumu and BpJpsiKplus channels in addition to the related to our analysis variables:
B+>JpsiK+
Main trigger used for this analysis:
 Up to run number 284484: HLT_mu4_mu6_bJpsimumu > Main stream
 From 284484 up to 302956: HLT_mu4_mu6_bJpsimumu_Lxy0 > Main stream
 From 302956 and beyound: HLT_mu4_mu6_bJpsimumu_Lxy0_delayed > Delayed stream
Main stream periods: 2015 (D,E,F,G,H,J), 2016 (A,B,C,D,E,F,G,I,K,L)
Delayed stream periods: 2016 (D,E,F,G,I,K,L)
path for data: /eos/atlas/atlascerngroupdisk/physbeauty/BsMuMuRun2/BsMuMuRel21Prod1/ntup/skimmed_[MC/data]/[For MC: Channel]/v3/
The used MC sample according to the Bmumu partial Run2 analysis is: DSID: 300404, events: 886359, candidates: 1238672
Ntuple variables in MC samples related to Jpsi:
Jpsi_iso_7_Chi2_5_LoosePt05 
Jpsi_a_2D 
Jpsi_eta 
Jpsi_MUCALC_massErr 
Jpsi_properTime 
Jpsi_PlngMin3D 
Jpsi_DR 
Jpsi_a_3D 
Jpsi_phi 
Jpsi_mass 
Jpsi_properTime_err 
Jpsi_PlngMax3D 
Jpsi_Lxy 
Jpsi_Chi2_PVSV_log1Dz 
Jpsi_fitChi2 
Jpsi_massErr 
Jpsi_properTime_sig 

Jpsi_Lxy_err 
Jpsi_Chi2_PVSV_log2D 
Jpsi_fitNDF 
Jpsi_minChi2MuonsIPtoAnyPV 
Jpsi_PlngMin2D 

Jpsi_Lxy_sig 
Jpsi_Chi2_PVSV_log3D 
Jpsi_MUCALC_mass 
Jpsi_pT 
Jpsi_PlngMax2D 

Ntuple variables in MC samples related to Jpsi Truth:
TRUTH_Jpsi_pT 
TRUTH_Jpsi_eta 
TRUTH_Jpsi_phi 
TRUTH_Jpsi_mass 
TRUTH_Jpsi_PDGID 
Ntuple variables in MC samples related to Bplus Truth:
TRUTH_B_pT 
TRUTH_B_vtx_x 
TRUTH_B_eta 
TRUTH_B_vtx_y 
TRUTH_B_phi 

TRUTH_B_mass 

TRUTH_B_PDGID 

Jpsi studies for variables
In this section we are going to show the studies performed on the Jpsi both in data and MC for checking the above mentioned variables:

Proper decay time distributions calculated with different mass values. The first plot is the proper decay time variable stored in the ntuple. The second is the proper decay time calculated with the MUCALC mass. The third is the proper decay time calculated with the Mass variable. The last one is with the value obtained from the PDG 
Bin per bin difference to compare the proper decay time distribution obtained from the variable in the ntuple with the distributions obtained from the different masses in the ntuple. Again Plot 1 is the Ntuple vs MUCALC calculation, Plot 2 is the Ntuple vs Mass, Plot 3 is the Ntuple vs the PDG value 
Difference and ratio for all the proper decay time calculations 
The MUCALC mass distribution for the 4 highest BDT bins (same BDT bins as Bmumu analysis. 
The MUCALC mass distribution for the 4 highest BDT bins taken from the paper pictures. Not very acqurate since it was taken my using an online tool for extracting points which means that clicking the points is not that acquare. 
Ratio plot for Ntuple value  Paper value with the uncetainty of clicking the value with low resolution from the picture 
Proper decay time at truth level for Bplus, calculated from the PV(x,y) position and the B(x,y) position 
Selection of proper decay time calculation
An important question to be asked is which of the available proper decay time calculations to use. In our ntuples 4 possible calculations can be used:
 Measured Lxy, Measured pT, Measured Mass (with Muon Spectometer = MUCALC)
 Measured Lxy, Measured pT, Measured Mass (only Inner Detector = VTX)
 Measured Lxy, Measured pT, Truth Mass (Mass taken from the MC = PDG mass with it's intrinstic distribution + Radiative tails)
 Measured Lxy, Measured pT, PDG mass (as a constant)
The first check we performed was to see what the properTime variable was using for the calculation. For this it was important to look a per event ratio between the properTime variable from the ntuple and the other available calculations. We performed the excerise on the MC sample for the BpJpsiKp for the Jpsi properTime.
Ratio per event for the proper time calculated with the MUCALC mass in the formula divided by the ntuple properTime variable 
Ratio per event for the proper time calculated with the VTX mass in the formula divided by the ntuple properTime variable 
Ratio per event for the proper time calculated with the Truth mass in the formula (with a PDG cut to ensure Jpsi masses) divided by the ntuple properTIme variable 
Ratio per event for the proper time calculated with the PDG value (without the intrinstic width) in the formula divided by the ntuple properTime variable 
from the plots above it can be shown that the ntuple variable properTime is being calculated with the use of the PDG value as a constant. This is a aligned with what was found in the ATHENA code for the derivation however from that side things were not that clear. Additionally, the small differences that are observed were concluded to be due to storage IO of the variable through the progress of the derivation code. Finally we confirmed also by looking in the ntuple making code that the calculation of the proper time in both the Jpsi and the B+ is performed by using the same type of mass.
After the validation now the next step was to compare the four proper decay time calculations with the truth proper decay time from the MC and by taking the difference and look at the resolution to identify the calculation with the best proper time resolution. Since, in the ntuple the truth Jpsi proper time is not there we had to calculated with the rest of the truth variables. For this we assumed that the Jpsi vertex ~ same with the B+ vertex in order to calculate the truth Lxy. The results can be shown in the following three plots:
Difference between the truth Jpsi proper time and the proper time calculated using the measured MUCALC mass. The resolution value is 0.02814 
Difference between the truth Jpsi proper time and the proper time calculated using the measured VTX mass. The resolution value is 0.02669 
Difference between the truth Jpsi proper time and the proper time calculated using the PDG value for the mass (without the instrinsic width, just the mean value). The resolution value is 0.0282 
From the study above it's clear that although the PDG value is the value used to perform the proper time calculation in first place the mass that produces the best resolution is the Jpsi VTX mass. The main reason for this is that the Lxy and pT for the Jpsi are calculated using information from the inner detector (tracks). That means that calculating the proper time with the VTX mass (which uses the same information) we introduce a correlated variable which means that some of the uncertainties are common and therfore cancelled. A confirmation can be seen from the fact that even when adding the MUCALC mass in the calculation the resolution is still better than the constanc PDG mass used in first place since again there is the correlation due to the inner detector information used.
B+ proper time resolution
The above procedure has been also applied for the B+ variables in the ntuple with the following results obtained.
Ratio per even for the proper time calculated with the B MUCALC mass in the formula divide by the ntuple properTime variable 
Ratio per even for the proper time calculated with the B VTX mass in the formula divide by the ntuple properTime variable 
Ratio per even for the proper time calculated with the B Truth mass in the formula divide by the ntuple properTime variable 
Ratio per even for the proper time calculated with the B PDG mass in the formula divide by the ntuple properTime variable 
The similar result between the TRUTH and the PDG mass calculation is due to the fact that the B+ mass is generated as a constant value in the MC without any width as the Jpsi. Regarding now the resolution studies the following plots where obtained:
Difference between the truth B proper time and the proper time calculated using the measured MUCALC mass. The resolution value is 0.08531 
Difference between the truth B proper time and the proper time calculated using the measured VTX mass. The resolution value is 0.08027 
Difference between the truth B proper time and the proper time calculated using the PDG value for the mass. The resolution value is 0.08126 
Difference between the truth B proper time and the proper time calculated using the TRUTH value for the mass. The resolution value is 0.08126 
Showing again that the VTX mass is the preferable mass to be used for the best proper decay time resolution. The reasons are exactly the same as above for the Jpsi. Finally we see again that PDG and TRUTH values for the resolution match exactly, as expected.
Bs lifetime distribution
In this section the distribution of the lifetime will be shown after applying different set of cuts in the Bs 2015/2016 data ntuple. This study was performed after the Rare decays meeting where the analysis plan was described.
2015/2016 analysis BDT cut (0.416)
Initially we tried to apply the BDT bin 3 BDT cut from the 2015/2016 analysis where in the signal region (SR:51665526MeV) we expect only clean Bs signal.
MUCALC mass, VTX mass, Lxy, ProperTime distributions for the Left SB (LSB: 47665166 MeV), Signal Region (SR: 51665526 MeV) and Right SB (RSB: 55265966 MeV), with the BDT Bin 3 cut (0.416) 
Proper time distribution in signal region for BDT bin 3 
from the plots above it can be seen that the number of events we expect for our proper decay time measurement is very few as expected leading to the result that the main source of uncertainties in the analysis will be the statistical uncertainties.
Rough BDT cut at 0.3
Following the identification of the proper time distribution on a bin where there is clean Bs signal we tried to find a BDT cut which is a good starting point for setting up the analysis procedure. For this reason we added on the top of the previous two plots the same regions with a BDT cut of 0.3 leading to the following results:
MUCALC mass, VTX mass, Lxy and ProperTime distributions for BDT bin 3 of the analysis and a BDT cut of 0.3 
Proper time distributions for the BDT bin 3 (RED) and BDT cut 0.3 (Yellow) in the SR of the 2015/2016 dataset 
Proper time distribution for the BDT cut 0.3 which is signal + background 
from the plots above it can be seen again that the dominant source in the effective lifetime studies is the background which is boosting the number of events in the SR massively. However we know that the signal contribution is going to be small and therefore dominated by statistics.
Bs invariant mass distribution and sPlot
For this study there is a detailed page BsPlot
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